Generic quantum spin ice

TL;DR

This paper extends gauge mean field theory to analyze the ground states of quantum spin ice with general exchange interactions, revealing new quantum spin liquid and quadrupolar ordered phases, especially in non-Kramers pyrochlores.

Contribution

It introduces a significant extension of gMFT to include additional exchange interactions, enabling analysis of more complex quantum spin ice models.

Findings

Identified three quantum ground states: U(1) QSL, antiferro-quadrupolar, and non-coplanar ferro-quadrupolar.

Found that frustrated XY exchange favors a pi-flux QSL with line degeneracy.

Enhanced stability of QSL due to emergent degeneracy in spinon excitations.

Abstract

We consider possible exotic ground states of quantum spin ice as realized in rare earth pyrochlores. Prior work in Phys. Rev. Lett. 108, 037202 introduced a gauge mean field theory (gMFT) to treat spin or pseudospin Hamiltonians for such systems, reformulated as a problem of bosonic spinons coupled to a U(1) gauge field. We extend gMFT to treat the most general, nearest neighbor exchange Hamiltonian, which contains a further exchange interaction, not considered previously. This term leads to interactions between spinons, and requires a significant extension of gMFT, which we provide. As an application, we focus especially on the non-Kramers materials Pr2TM2O7 (TM=Sn, Zr, Hf, and Ir), for which the additional term is especially important, but for which an Ising-planar exchange coupling discussed previously is forbidden by time-reversal symmetry. In this case, when the planar XY exchange is unfrustrated, we perform a full analysis and find three quantum ground states: a U(1) quantum spin liquid (QSL), an antiferro-quadrupolar ordered state and a non-coplanar ferro-quadrupolar ordered one. We also consider the case of frustrated XY exchange, and find that it favors a pi-flux QSL, with an emergent line degeneracy of low energy spinon excitations. This feature greatly enhances the stability of the QSL with respect to classical ordering.